Seriously!!!

STOP NOW!!! Tell the shop to not do anything!

Get the proper counter-weighted flexplate for the engine. If you need a LA 360 balance plate it's either a 10236 (727) or a 10239 (904).
The shop DOES NOT need your TC with the correct flexplate.

Make sure you have the proper balancer for the engine as well. A 318 balancer won't work on a 360 especially if the shop says they need to add weight to the converter, thus, external balance.

Not sure how many times one person, 73AbodEE, can say the same thing. :)